Boehner assured the two girls that he was still working to push immigration reform through.

"I'm trying to find some way to get this thing done," he said. "It's, as you know, not easy -- not going to be an easy path forward. But, I've made it clear since the day after the election that it's time to get this done."

Lima, whose father is an illegal immigrant who could be deprted, told Boehner her story.

"How would you feel if you had to tell your kids at the age of 10 that you were never coming home?" she asked.